Matrix Valued Spherical Functions Associated to the Three Dimensional Hyperbolic Space
| dc.creator | Grunbaum, F. A. | |
| dc.creator | Pacharoni, I. | |
| dc.creator | Tirao, J. | |
| dc.date | 2002-03-20 | |
| dc.date.accessioned | 2026-07-07T04:47:11Z | |
| dc.date.available | 2026-07-07T04:47:11Z | |
| dc.description | The main purpose of this paper is to compute all irreducible spherical functions on $G={SL}(2,{\mathbb C})$ of arbitrary type $δ\in \hat K$, where $K={SU}(2)$. This is accomplished by associating to a spherical function $Φ$ on $G$ a matrix valued function $H$ on the three dimensional hyperbolic space ${\mathbb H}=G/K$. The entries of $H$ are solutions of two coupled systems of ordinary differential equations. By an appropriate twisting involving Hahn polynomials we uncouple one of the systems and express the entries of $H$ in terms of Gauss' functions ${}_2F_1$. Just as in the compact instance treated in [GPT] there is a useful role for a special class of generalized hypergeometric functions ${}_{p+1}F_p$. | |
| dc.description | 55 pages | |
| dc.identifier | https://arxiv.org/abs/math/0203211 | |
| dc.identifier | http://arxiv.org/abs/math/0203211 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63615 | |
| dc.subject | Representation Theory | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 22E30; 22E46; 33C45 | |
| dc.title | Matrix Valued Spherical Functions Associated to the Three Dimensional Hyperbolic Space | |
| dc.type | text |